Numerical Simulation Of Elliptic Mild-Slope Equation And Near-shore Wave-induced Current In Unstructured Grid

Offshore area has inseparable relationship with human life and economy development. Near-shore wave-current field affect the programming and design of hydraulic construction and is the important cause to nearshore sediment transport and pollutant transport.In this paper,the elliptic mild-slope equation mathematical model and the near-shore wave-induced current mathematical model is constructed by finite volume method in unstructured grid.Under unstructured grid,the elliptic mild-slope equation mathematical model which considers wave breaking is constructed.The model's control equation is dispersed by finite volume method.The GPBiCG(m,n) interactive algorithm is used to calculate the dispersed equation.The methods of boundary conditions under unstructured grid are given,which make the dispersion of element near the boundary consistent with inner element.The boundary conditions are more convenient and uniform.The linear and nonlinear dispersion relations of wave are respectively applied to the calculation of wave transformation over the circle shoal and elliptic shoal.Then the numerical results are compared with the experimental results,and the influence of the dispersion relations' nonlinearity on calculation result is analyzed.Numerical result proves the precision and applicability of the elliptic mild-slope equation mathematical model.This model is also applied to the Memos physical model experiment and Jun-nlng Pan's physical model experiment which have irregular boundary,and the numerical results calculated by nonlinear dispersion relations are in good agreement with measured results.The numerical result proves the reliability of this model and it's adapted to the complex boundary.Under unstructured grid,the near-shore wave-induced current mathematical model is constructed by adding the wave radiation stress to the source terms oft he 2D shallow water equation.The time dispersion is made by Euler forward schemes,and the spatial dispersion is made by explicit schemes with finite volume method.Based on the definition of wave radiation stress,the wave radiation stress caused by wave breaking is directly calculated with wave potential function from the elliptic mild-slope equation.It avoids the difficulty to calculate the wave direction.Simulate the wave-induced current near the offshore artificial island,and validate the mathematical model with the measure data.The regular wave-induced longshore current is calculated under action of regular wave with various grade,wave height,wave period and the bottom friction,and the numerical results are in good agreement with experimental results. The numerical result proves the reliability of the near-shore wave-induced current mathematical model and it's adapted to the complex boundary.